To determine the temperature at which an exothermic reaction ceases to be spontaneous, we need to calculate the Gibbs free energy change (ΔG) and use the equation ΔG = ΔH - TΔS.
Given that ΔH = -71 kJ/mol and ΔS = -58 J/K·mol, we can calculate ΔG at different temperatures to determine the temperature at which the reaction becomes non-spontaneous.
At a temperature of 0 K, ΔG = ΔH, since TΔS = 0. Thus, ΔG = -71 kJ/mol.
As the temperature increases, TΔS becomes more negative, which means that ΔG becomes more negative, making the reaction more spontaneous.
At a certain temperature, however, ΔG will become positive, which means that the reaction is no longer spontaneous and will not proceed on its own. This temperature can be found by rearranging the equation ΔG = ΔH - TΔS to T = ΔH / ΔS, and substituting the known values for ΔH and ΔS:
T = ΔH / ΔS = -71 kJ/mol / (-58 J/K·mol) = 1230 K
So, the reaction will cease to be spontaneous at a temperature of approximately 1230 K.